A survey was done recently by the Royal Bank with Ipsos Reid (reported in Globe and Mail Aug 16 2010) about financial issues that university students face. (Data used here is based on that survey, but randomized to be still within the margin of error of that survey.) The survey found that 73 % of university students did not use a budget. Consider another survey, using 470 university students which found that 356 of these were not using a budget.
Find the mean and standard deviation for the number of university students not using a budget.
Mean =
Standard deviation =
what is t
To find the mean and standard deviation for the number of university students not using a budget, we can use the given data.
First, let's define the variables:
- N = total number of students in the survey = 470
- X = number of students not using a budget = 356
The mean (μ) can be calculated using the formula:
μ = X / N
Substituting the values, we have:
μ = 356 / 470
To find the standard deviation (σ), we need to know the proportion of students not using a budget in the population. However, since we don't have that information, we cannot calculate the exact standard deviation.
We can estimate the standard deviation using the formula for the sample proportion:
σ = sqrt((p * (1 - p)) / n)
Where:
- p = proportion of students not using a budget in the sample = X / N
- n = sample size = N
Substituting the values, we have:
σ = sqrt((356/470) * (1 - 356/470) / 470)
Since the data is randomized within the margin of error, we can assume the standard deviation to be the same as the margin of error provided in the original survey.
Note: It's important to remember that this calculation assumes the survey sample is representative of the entire population of university students.